An inversion formula for the dual horocyclic Radon transform on the hyperbolic plane

    Authors

    A. Katsevich

    Comments

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    Abbreviated Journal Title

    Math. Nachr.

    Keywords

    dual Radon transform; horocycle; hyperbolic plane; inversion formula; CONSTANT CURVATURE; SPACES; Mathematics

    Abstract

    Consider the Poincare unit disk model for the hyperbolic plane H-2. Let Xi be the set of all horocycles in H 2 parametrized by (theta, p), where e(i theta) is the point where a horocycle xi is tangent to the boundary vertical bar z vertical bar = 1, and p is the hyperbolic distance from xi to the origin. In this paper we invert the dual Radon transform R* : mu(theta, p) - > mu(z) under the assumption of exponential decay of mu and some of its derivatives. The additional assumption is that P-m(d/dp) (mu(m)(p)e(p)) be even for all m is an element of Z. Here P-m (d/dp) is a family of differential operators introduced by Helgason, and mu(m) (p) are the coefficients of the Fourier series expansion of mu(theta, p). (c) 2005 WILEY-VCH Verlag GmbH C Co.

    Journal Title

    Mathematische Nachrichten

    Volume

    278

    Issue/Number

    4

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    437

    Last Page

    450

    WOS Identifier

    WOS:000228064000008

    ISSN

    0025-584X

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